I guess it depends on the baby\person.
Yes, this. Again my anecdote was DD having an operation to have an abscess in her mastoid complex removed at 14 months, so a GA with an op, followed by 4 days in hospital on a IV antibiotics. I had to hold her down while the Doctor (who I wanted to smack) checked the drain in her scull while DD screamed blue murder (as you would). DD was fine immediately afterwards. In fact, she was better than she had been previously, and being ill in that way had clearly slowed her down from exploring the world in the way that she'd like.
She also had an emotionally unavailable mother for the first 2 years of her life, and then a volatile, confusing mother for another year when she was 4/5. (I'm a lot better now, following a shedload of treatment.)
She remains the most confident child I have ever known in my life. It's almost freakish.
DS has not been left unscathed by it all, and is quite anxious (though never had an op).
Stuff happens - children react in the way that they react. He may well have been affected, but if this wasn't evident in his behaviour, I don't know how else you'd assess it.